Question: Simplify the following expression: $\dfrac{3n^4}{12n}$ You can assume $n \neq 0$.
Answer: $ \dfrac{3n^4}{12n} = \dfrac{3}{12} \cdot \dfrac{n^4}{n} $ To simplify $\frac{3}{12}$ , find the greatest common factor (GCD) of $3$ and $12$ $3 = 3$ $12 = 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(3, 12) = 3 $ $ \dfrac{3}{12} \cdot \dfrac{n^4}{n} = \dfrac{3 \cdot 1}{3 \cdot 4} \cdot \dfrac{n^4}{n} $ $\phantom{ \dfrac{3}{12} \cdot \dfrac{4}{1}} = \dfrac{1}{4} \cdot \dfrac{n^4}{n} $ $ \dfrac{n^4}{n} = \dfrac{n \cdot n \cdot n \cdot n}{n} = n^3 $ $ \dfrac{1}{4} \cdot n^3 = \dfrac{n^3}{4} $